Multidisciplinary Design Approach
and Safety Analysis of ADSR Cooled
Dit proefschrift is goedgekeurd door de promotoren: Prof. dr.ir. A.H.M. Verkooijen Prof. dr.ir. T.H.J.J. Van der Hagen Samenstelling promotiecommissie: Rector Magnificus Voorzitter Prof.dr.ir. A.H.M. Verkooijen Technische Universiteit Delft, promotor Prof.dr.ir. T.H.J.J. Van der Hagen Technische Universiteit Delft, promotor Prof.dr.ir. R.F. Mudde Technische Universiteit Delft Prof.dr.ir. I.M. Richardson Technische Universiteit Delft Prof.dr. J. Martinez‐Val ETSII, Madrid, Spanje Dr. H. Ait Abderrahim Studiecentrum voor Kernenergie, Mol, Belgie Dr.ir. D. Lathouwers Technische Universiteit Delft Copyright © 2007 by Carlos Alberto Ceballos Castillo and IOS Press
Summary
Nuclear waste is composed of transuranic elements (plutonium and minor actinides) and fission products. The separation of plutonium from minor actinides in the nuclear waste offers a more efficient utilization of resources because plutonium can be recycled as fuel in different reactors. Similarly, the transformation of the minor actinides in lighter elements with transmutation reactions is a method to reduce the storing time and the amount of waste to be stored in the geological repository.
Transmutation can be achieved in all types of reactors ‐ thermal systems, fast systems, critical and sub‐critical systems (Gudowski et al., 2001). Fast spectrum systems have significant advantages because they offer higher transmutation efficiency in comparison to thermal systems (OECD/NEA, 2002). However, the addition of actinides to the fuel has adverse effects on safety parameters: the fraction of delayed neutrons and the Doppler coefficient are reduced (Eriksson et al., 2005). This parameter is very important to assure the dynamic control and safe operation of a critical reactor and for this reason the actinide content in the fuel of critical reactors has to be limited.
Alternatively, if the reactor is subcritical and an external neutron source is supplied, the system would be able to operate with a steady power level without a self‐sustained chain reaction (Rubbia et al., 1995). In this way, the shutdown of the external source gives the possibility for rapid control of any undesired power excursion in the transmuter. This novel reactor concept has been introduced as the Accelerator Driven Subcritical Reactor (ADSR).
different viewpoints. However, there are many technical issues to be solved before an ADSR system is realized.
The development of the ADSR depends on the successful integration of different systems, for which a safety strategy has to be adapted. This dissertation contributes to the development of the ADSR technology by studying two important safety aspects: the time‐dependent response during transient conditions and its influence over the structural integrity. For this purpose, thermalhydraulics, neutronics and structural models of the reactor are integrated.
The results have shown that a subcritical reactor is remarkably effective to overcome transients involving criticality risk. However, core damage and/or melt down are evident if the beam is not shutdown. Negative reactivity feedbacks do not reduce the power significantly and since, large percentage of heat is not efficiently removed, the structural integrity is exposed.
Natural circulation is not helpful in view of the fact that the mass flow rate is dependent on the density difference between the hot and cold legs. During transients, it can occur than the hot leg becomes cooler and the cold leg gets hotter ( e.g. during a a loss of heat sink transient), in this case, the buoyancy force changes direction working against the inertial force. If natural circulation is enhanced with a gas‐lift pump, the power rate of the reactor can be increased. Still, the oscillatory nature of the loop system is pronounced by gas density changes during temperature transients. This, subjects the mechanical components to higher thermal stress cyclic rates increasing the fatigue damage.
Another technical disadvantage of the buoyancy driven liquid metal reactors becomes the large temperature difference across the core, which increase the severity of thermal shocks. This is especially critical when looking at the beam trip frequency of current accelerators. A non‐conservative estimate shows that the reliability of the accelerator should be increased by a factor of 5 in order to avoid cladding failure during the first year of operation.
Samenvatting
Kernafval bestaat uit transuranen (plutonium en “minor actinides”, hierna aangeduid als MA) en splijtingsproducten. Het scheiden van plutonium van MA in het kernafval leidt tot een efficiënter gebruik van grondstoffen omdat plutonium gerecycleerd kan worden in diverse/verschillende (typen) reactoren. Tevens is de transmutatie van MA tot lichtere elementen een methode om de benodigde opslagtijd en de hoeveelheid afval binnen een geologische opslag te verkleinen.
Transmutatie kan worden bereikt in diverse reactortypen – thermische systemen, snelle systemen, kritieke en subkritieke systemen (Gudowski et al., 2001). Snel‐spectrum systemen hebben grote voordelen omdat deze een groter transmutatievermogen hebben in vergelijking met thermische systemen (OECD/NEA, 2002). Echter, de toevoeging van actiniden aan de splijtstof heeft een negatief effect op veiligheidsgerelateerde parameters: de fractie vertraagde neutronen en de Doppler coëfficiënt zijn kleiner (Eriksson et al., 2005). Deze parameters zijn bijzonder belangrijk om de dynamische controle en veilig bedrijf van een kritieke reactor en vanwege dit feit dient de actinide concentratie in de splijtstof beperkt te blijven. In geval van een subkritiek systeem waar een externe neutronenbron wordt gebruikt kan het systeem een constant vermogen leveren zonder een zichzelf in stand houdende kettingreactie (Rubbia et al., 1995). Afschakeling van de externe neutronenbron kan dan op korte termijn eventueel optredende vermogensoscillaties controleren. Dit reactor concept is eerder geïntroduceerd onder de naam “Accelerator Driven Subcritical Reactor” (ADSR).
In dit proefschrift wordt een bijdrage geleverd aan de ontwikkeling van ADSR technologie door twee veiligheidsaspecten te bestuderen: het tijdafhankelijk gedrag onder diverse condities en de invloed hiervan op de structurele integriteit. Hiervoor zijn modellen voor neutronica, thermohydraulica en mechanische analyse geïntegreerd.
De resultaten tonen aan dat een subkritieke reactor opmerkelijk effectief is in het ondervangen van ongevalscenario’s met een criticiteitsrisco. Schade aan de reactorkern of het smelten ervan kan echter voorkomen als de bron niet tijdig afgeschakeld wordt. Negatieve terugkoppeling van de reactiviteit reduceert het vermogen niet significant en omdat een groot gedeelte van de warmte niet afgevoerd wordt de mechanische stabiliteit negatief beïnvloed.
Natuurlijke circulatie is geen uiteindelijke oplossing vanwege het feit dat de massastroom afhankelijk is van de hete en koude secties. Gedurende transiënten kan het voorkomen dat de hete sectie kouder wordt dan de koude sectie (bv gedurende een ongeval met verlies van warmteafvoer) waardoor de drijvende kracht van richting veranderd en de massastroom doet afnemen. Wanneer natuurlijke circulatie wordt verhoogd met een “gas‐lift” pomp is het mogelijk het reactorvermogen te verhogen. Het oscillerende gedrag van de koellus is echter sterk aanwezig gedurende temperatuur transiënten vanwege
dichtheidveranderingen van het ingebrachte gas. Deze
temperatuursveranderingen stellen de mechanische componenten bloot aan thermische stress waardoor de kans schade door moeheid toeneemt.
Een ander technisch nadeel van een natuurlijke circulatie vloeibaar metaal gekoelde reactor is het grote temperatuurverschil over de kern waardoor de hevigheid van thermische schokken toeneemt. Dit is met name belangrijk i.v.m. de frequentie van versnellerafschakelingen. Een voorzichtige schatting leert dat de betrouwbaarheid van versnellers met een factor 5 dient toe te nemen om falen van de cladding te voorkomen gedurende het eerste jaar van reactorbedrijf.
1.1 Sustainable Nuclear Energy
Nuclear energy is an air pollution free technology with the potential to satisfy the world’s energy demands for many centuries. However, some concerns about the use of nuclear energy have to be further developed in order to recognize nuclear energy as a sustainable option. These concerns are the use of nuclear energy for weapons, the risk of accidents with radioactivity release and the waste management.
Nuclear waste is composed of trans‐uranic (TRU) elements and fission products. The TRU are the result of neutron capture in the fuel and subsequent decay. They can be separated in Pu and minor actinides (MA). The fission products are fragments produced during the fission process. Most of the fission products are short‐lived (less than 300 years) in comparison with the TRU elements, which can take thousands of years to reach the reference radiotoxicity level (ENEA, 2001).
Two methods are considered for managing radioactive waste: i) geological disposal, which consists of isolating the waste from the biosphere by placing it in a safe geological formation and wait for it to decay. The geological formation and a good container design have to assure the isolation of waste for a long period of time. These issues raise uncertainty about the future circumstances and the economical sustainability of this solution. ii) the separation of plutonium from MA and transformation of the MA in lighter elements with transmutation reactions before storing. The lighter elements have shorter half‐ lives and in this way, they would need to stay for a considerably shorter time in the repository. At the same time, the generation of electricity from MA is a more efficient utilization of resources.
All types of reactors can be used to transmute the MA ‐ thermal systems, fast systems, critical and sub‐critical systems (Gudowski et al., 2001). Fast spectrum systems have significant advantages because they offer higher transmutation efficiency in comparison to thermal systems (OECD/NEA, 2002). However, the addition of actinides to the fuel has adverse effects on safety parameters: the fraction of delayed neutrons and the Doppler coefficient are reduced (Eriksson
et al., 2005). These parameters are very important to assure the dynamic control
Alternatively, if the reactor is subcritical and an external neutron source is supplied, the system would be able to operate with a steady power level without a self‐sustained chain reaction (Rubbia et al., 1995). In this way, the shutdown of the external source gives the possibility for rapid control of any undesired power excursion in the transmuter. Last, the possibility of Plutonium recovery within a closed and controlled fuel cycle minimizes the risk of using it for weapons proliferation.
1.2 ADSR Role in the Nuclear Fuel Cycle
The transmutation efficiency is very important in any fuel cycle strategy. The efficiency is connected to the energy spectrum, burn‐up time and cost to transmute the waste. Fast reactors and ADSR will play an important role in this regard. The selected fuel cycle strategy may be suited to different performance requirements like the flexibility, the technological requirements, the proliferation, the economics, etc. A study carried out by OECD/NEA (2002) compared two waste management approaches: one considers plutonium as a by‐product from light water reactors (LWR) and separates it from the minor actinides stream. The other approach re‐processes them together. The second option is attractive because it enhances proliferation resistance but the first option offers a more economic competitiveness. These two approaches can be accommodated in different fuel cycle strategies according to technological and/or economical challenges. The schemes investigated by OECD/NEA are presented in figure 1.1, the figure shows 5 different transmutation strategies relevant to the future requirements.
Important conclusions of NEA’s investigation are that all transmutation strategies with multiple recycling of the fuel can achieve similar radiotoxicity reduction in the long‐term waste radiotoxicity. These strategies can achieve a hundred reduction factor in the long‐term waste radiotoxicity and even higher for actinides inventory reduction. Partially closed cycles are a near‐term transmutation option, but they do present a factor of two less reduction than the fully closed strategies. Fully closed cycles might be realised with a 10‐20% increase of electricity cost. For partially closed cycles the increase is about 7% of the electricity cost with regards to the once through cycle.
In a similar study, Cometto et al., (2004) have presented comparable results. They suggest that due to its economical and technological requirements, ADSR’s are best suited to work as minor actinide burners in the double strata cycle, whereas critical FR’s are better for Pu and MA together in a TRU burning strategy. Another similar study by Hoffman and Stacey, (2002) declares that an ADSR would be capable of a net TRU destruction rate 2 to 3 times larger than a critical FR (similar to what NEA has reported). This advantage is only visible in the use of non‐fertile TRU in the ADSR. On the other hand, if energy is produced, the ADSR would account for 25% of the total generated power while the FR would produce a 45% of the total power.
The spallated neutrons will start a chain reaction in the nuclear core and the rate will be dependent on the proton flux from the accelerator. The spallation target would be located in the middle of the reactor core. In this way, effective control can be executed through the accelerator’s proton current.
A schematic drawing of an ADSR system is shown in figure 1.2, identifying its major components. A high power particle accelerator produces energetic protons that hit a heavy metal target to produce neutrons. The neutrons feed the nuclear fission process of a subcritical reactor where nuclear waste has been placed. A conventional power cycle is added to remove heat and generate electricity.
Figure 1.2 Scheme of the ADSR (source: OECD/NEA,2002)
Different ideas have been proposed for ADSR concepts based on fundamental physical properties such as neutron energy spectrum ‐ fast and thermal (Gudowski et al., 2001), fuel type ‐ solid, liquid (Takano and Nishara, 2002; Nifenecker et al., 2003) and coolant – lead‐bismuth eutectic (LBE), lead, sodium, and gas (Kerkdraon et al., 2003; Nifenecker et al., 2001). Most international programs seem to be evolving toward fast‐spectrum, liquid metal‐cooled sub‐ critical assemblies driven by large linear accelerators (Sasa et al., 2004; ENEA, 2001). For target materials, heavy metal such as lead‐bismuth (Pb‐Bi) or tungsten are proposed (Seltborg et al., 2003; Vickers, 2003).
Although accelerator development has advanced and linear accelerators are capable to accelerate protons to several GeV, the frequently repeated beam trips can significantly damage the reactor structures, the spallation target and the fuel, decreasing the ADSR plant availability. The other reliable option for high‐ power beams is to use cyclotrons, however, they are limited to maximum energies of about 1 GeV and electric currents of a few mA. This may be sufficient to drive a small ADSR but insufficient for large applications (Ponomarev, 2002). The accelerator also has to be capable to produce a stable and reliable low and high intensity proton beam, which is needed for the start process and the steady operation. The reliability requirements are related to the number of allowable beam trips and its effect on plant parameters deviation (thermal power, primary flow, pressure, temperature). The spallation target design for an ADSR should optimize the neutronic efficiency, the material properties and thermal‐hydraulics, since it is simultaneously subject to severe thermal‐mechanical loads and damage due to high‐energy heavy particles ‐ protons, spallation and fission neutrons (Tak et al., 2005).
The selected subcriticality level must be properly balanced considering economical reasons like the desire to construct a system with a low beam power, and safety reasons like that a small subcriticality level implies an increased risk of approaching criticality under transient conditions, but also larger effects of the negative feedbacks. An adequate level of subcriticality can be achieved by conservatively estimating the positive reactivity insertions. They are associated with incidents and accident conditions such as fuel, coolant and structural materials temperatures variation, coolant voiding and properly choosing the allowable range of normal operating conditions (Perdu et al., 2003). An additional requirement is the compensation of fissile material burn‐ up indicating that an operational range to maintain the steady required power level is needed, as well as to execute a careful reactivity monitoring to assure safe operation (Baeten and Abderrahim, 2004; Bianchi et al., 2005).
points are disadvantageous during shutdown and refuelling since primary coolant freezing must be avoided.
The core can be cooled either by forced or natural circulation. The use of natural circulation is preferred since it eliminates the occurrence of loss of flow accidents and the cost involved with the operation and maintenance of redundant systems. Natural circulation was an important inherent safety feature proposed in the first concept of ADSR (Rubbia et al., 1995) and it is being considered to implement it in the first experimental XADS facility (Ansaldo, 2001; Cinotti, 2004). The ADSR can be connected to a conventional power cycle with an intermediate cooling circuit or directly to the steam generator. The design of the intermediate heat exchanger or steam generator and placement inside the reactor vessel is constraint by the vessel size, which is equally constraint by the capital cost and the compactness desired features of such a plant (Salvatores, 2005).
Regarding fuels: oxides and nitrides are considered as the most promising fuel materials (ENEA, 2001). Oxide phases have the advantage of high chemical stability and relative simple handling and fabrication, which is very important for actinides handling. However, the relatively low thermal conductivity of oxide materials leads to high operating temperatures. Composites (ceramic‐ metal or ceramic‐ceramic) are preferred to provide the high heat transfer rates required to avoid large peaking temperature in the fuel: composite with steel (CERMET) or MgO (CERCER) are the first referenced options for advanced fuels (Eriksson et al., 2005; Chen et al., 2004; Maschek et al., 2003). Using liquid fuels would avoid burn‐up reactivity changes by adding fissile material on‐line and removing poisons. However, compared to solid fuels, liquid fuels present much larger unknowns associated with material compatibility and operation. R&D on these key issues and the system integration are the most important steps towards the ADSR demonstration. These developments have to be realized with economic competitive advantages and maximizing safety characteristics like inherent and passive safety systems.
1.4 Motivation
basic requirements for this philosophy have to cope with the general guidelines of nuclear reactor safety – the protection of people and the environment by establishing and maintaining effective defenses against radiological hazards (IAEA, 1993).
The best procedure for optimizing the design is a conscientious safety analysis of the system. The most traditional technique for verifying and demonstrating the safety of any nuclear facility is the defence in depth (IAEA, 1996). It is implemented by listing the initiating events (internal and external hazards) and classify them by categories regarding their expected frequency of occurrence. The events are analyzed with stringent rules. The prevention has to be pursued by passive control, active actions and inspection activities. As a second step, the mitigation of the accident is required despite the high prevention levels are achieved by the first analysis. The process is complemented by a line of defence method which defines the safety requirements for the safety systems. They can be divided on three types: the preventive measures to avoid initiating events, the active and passive measures and the inherent behavior or resistance by natural behavior.
Recent strategies to reduce or exclude potential accidents and improve reactor economy involve the use of buoyancy driven flows in the reactor primary cooling circuit. In principle, the implementation of natural circulation in a liquid metal cooled nuclear reactor could suppress the dependence on external pumps and assure a safe and reliable operation. Even in a forced circulation system, the capability of the coolant to develop natural circulation is of great interest for decay heat removal of the core after reactor shutdown. The advanced LWR adopts natural circulation as its cooling principle and are projected to cover the small and medium power ranges from the LWR park. Liquid metal fast reactors (LMFR) and ADSR cooled by natural circulation seem to have a more narrow range of operation (Davis et al., 2002; Chang et al., 2000), as the coolant does not undergo phase change in the core. Therefore, the temperature difference across the core of a liquid metal reactor exceeds by far the temperature difference of the LWR and its technical demands to the structural components become more stringent.
neutron kinetics. The results were optimistic and the idea is being further developed as the experimental XADS facility from the European Union (Ansaldo, 2001). Analysis of transients has also been carried out for the XADS (Coddington et al., 2004). Simplified models for the two‐phase flow in the riser and detailed modeling of the reactor vessel auxiliary cooling system (RVACS) have shown that the delay before beam shut‐off after initiation of loss of heat sink accident is a critical parameter (Carlsson and Wider, 2002). The successful utilization of natural circulation in a large scale ADSR will imply the reduction of risks during operation. Hence, it is of great interest to study the ADSR design and safe operation focusing on the possible implementation of a natural circulation system for an industrial scale ADSR.
Regarding the dynamics of a sub‐critical system, the first concern is the control of power and monitoring of reactivity. The system needs to shut down the beam if an unwanted variation of core parameters is detected (neutron flux, primary flow, temperature). The reactor has to remain subcritical at any conceivable state, an adequate margin to criticality is needed for any event like the positive reactivity insertions associated with changing conditions from fuel, coolant and structural materials temperatures variations. In the event of unprotected transients (beam remains on) a reliable safety related beam shutdown system is desirable (Eriksson and Cahalan, 2002), as well as a long grace time period for the system to act. Transient analysis of the ADSR would allow us to understand and predict the reactor response under different scenarios threatening the ADSR safe operation.
1.5 Objectives and Scope
The goal is to contribute to the development of ADSR technology by studying two main safety aspects: the transient response and its impact on the structural integrity. For this purpose, the neutronic, thermalhydraulic and mechanical systems have to be integrated.
The thermalhydraulic system plays an important role in the performance and the safety. Hence, it is a primary objective to develop a better understanding of the natural circulation thermalhydraulic systems for a liquid metal cooled ADSR. The feasibility and reliability of a high power liquid metal cooled buoyancy driven reactor has to be investigated. Likewise, the effects of the thermal coupling with neutron kinetics verified. Additionally, the interaction of the beam with the thermalhydraulic and neutronic systems, as well as with the mechanical components has to be reviewed. This work will develop a better understanding of the ADSR design parameters, characteristic dynamic response and provide information for future optimization and design guidelines.
The methodology employed set the following steps: first, to build a thermalhydraulic model of the ADSR and to couple it with a neutronic dynamic model. Then, to study the thermalhydraulic behavior during steady state and transient conditions, evaluating the modeling results within the framework of safety. Subsequently, to integrate the mechanical systems in the model and assess their structural integrity. As a result, to identify routes for the development of the ADSR technologies and safety guidelines.
1.6 Outline
This thesis presents the work‐study on safety analysis of ADSR cooled by buoyancy driven flows. The thesis is outlined as follows:
In chapter 3, a detailed description of the systems interaction is described. Physical models for neutronic, fuel pin heat transfer and thermalhydraulic models are presented. The modeling approach and the model validation are discussed as well. Special interest is shown in the thermalhydraulic modeling approaches in which a simplified and a detailed geometrical description of the core have provided different levels of problem understanding and information.
Chapter 4 explores the feasibility of cooling a liquid metal ADSR using buoyancy driven flows. The first part explains the nature of the natural circulation single‐phase reactor and its scaling principles. Then, it discusses the implementation of the buoyancy enhancement with gas injection in order to increase the core power capacity. The study takes as a baseline the design from MIT and INL (Davis et al., 2002) for a single‐phase natural circulation lead‐ bismuth actinide burner. At the end of the chapter, some observations are introduced regarding the hydrodynamic effects on flow and cooling performance.
Chapter 5 presents the transient analysis of the scenarios established in chapter 2. The event consequences are determined and valued with the safety criteria that were discussed in chapter 2 as well. The results obtained with a one‐ dimensional thermalhydraulic model compare two concepts: the single‐phase and the two‐phase buoyancy driven flow reactors. The results have characterized the dynamic response from every system. Then, a detailed two‐ dimensional model of the core demonstrates the safety advantages of the two‐ phase concept and provides information for the structural integrity assessment of the fuel pin cladding. Chapter 6 evaluates the impact of beam trips frequency on the ADSR lifetime. The first section describes a thermal‐structural stress model suggested to study creep‐fatigue interaction in the fuel pin cladding. Then, thermal‐stress transient analysis is carried out together with creep analysis and the results are discussed. The structural integrity assessment is derived with engineering rules for reactor design recommended by the ASME Boiler and Pressure Vessel Code – Case N47.
armaments, no one in this world would go to bed hungry” James Morris, head of the WFP
2 Safety Considerations for Design
and Control
2.1 Introduction
The operation principle of the ADSR has been described in detail in section 1.3. By conceptual definition, the ADSR is an inherent safe reactor, because the subcritical state provides a sufficient margin to cope with the reduction on the delayed neutron fraction and the Doppler effect. In case of a positive reactivity insertion, the subcritical state assures that the reactor does not become prompt supercritical and if the controller foresees any risk, it can order the proton beam to stop, bringing the reactor to decay power conditions.
The safety characteristics of the ADSR should also consider different aspects involved in the system integration. For example, the heat removal by the thermalhydraulic system has an effect on neutronic performance during transient conditions. In similar way, the rate of heat removal by the thermalhydraulic system has an effect on structural components lifetime. In addition, the design has to exclude any potential hazards from reactivity excursions and tolerate much more transients than the actual nuclear plants. This is due to the larger amount of beam interruptions.
For study purposes, some relevant parameters were identified, constrained and grouped to form the design limits and safety limits, which describe the safety envelope for the ADSR. These parameters have been grouped according to their nature in: neutronic, thermalhydraulic and mechanical systems constraints.
normal operating conditions like start up, shutdown, loading and abnormal reactivity evolutions due to burn up. For these purposes, detection and control systems and methods are investigated. SAFETY ENVELOPE Neutron Kinetics Constraints Thermalhydraulic Constraints Mechanical Constraints Controllability Integrity Figure 2.1 Definition of physical constraints and safety envelope for the ADSR operation The integrity relates to the capacity to withstand any circumstances risking the lifetime and availability of the reactor. The structural components should resist to mechanical and thermal loads and their time‐dependent effect during operation and transient events. The loading type could provoke unfavorable or excessive requirements delivering partial or total failure of the component. Moreover, a loss of controllability sometimes has as a consequence on loss of integrity and viceversa. A change in some thermalhydraulic parameters could indirectly lead to controllability or integrity losses, by interaction with the neutron kinetics and mechanical systems.
The safety strategy for the ADSR should provide different mechanisms to influence the constrained parameters (top) and keep them below certain limits. These safety limits define the safety envelope for the safe operation. When the safety limits are exceeded, the safety envelope is abandoned and the controllability and integrity are exposed (bottom).
In the following sections, we discuss the ADSR safety issues using the systems classification from figure 2.1. From these, one should be able to identify the parameters that constraint the reactor safe operation and to differentiate which are design constraints and which, safety constraints. Afterwards, one can introduce margins or limits to these parameters and set a number of hypothetical scenarios for the safety analysis.
2.2 Neutronic Issues
Neutron Kinetics
The primary goal on the design of the ADSR is to maximize the transmutation rate. For this reason, fuel free of 238U or 232Th should be used. As a consequence, the delayed neutron fraction is considerably reduced and the Doppler effect is small. The impact on safety parameters is strong and the requirement of a subcritical state, to assure inherent safety is desired. Maschek et al., (2003) have calculated the kinetic parameters of a fuel mixture consisting of 25% Pu and 75% MA, for a 1200 MWth core power at a subcritical level of keff = 0.98. Table 2.1 shows the deterioration of the kinetic parameters of the subcritical reactor in comparison with the Superphenix fast reactor.
Table 2.1 Comparison of fuel kinetics parameters between an ADSR and the Superphenix FR
Kinetic Parameters ADSR Superphenix
Doppler constant [pcm/K]1 ‐100 ‐860
βeff [pcm] 150 400 neutron generation time [s] 2x10‐7 4x10‐7
The effect of these parameters on the reactor kinetics, can be studied through an analytical solution of the point kinetics equations for one delayed neutron group. In steady state conditions, the neutron density is proportional to the
source intensity and the time constant is the prompt neutron generation time. The steady state neutron density is 0 0 0
ρ
= −
q l
n
(2.1)where, n0 is the neutron density, ρ0 the initial reactivity, l the time constant of the prompt neutrons and q0 the external neutron source per unit time. If one takes the ratio of two different steady states, the result would be proportional to the source change, and the initial reactivity as 0 1 1 0 0 1
⎛
⎞
=
⎜
⎝
⎠
n
q
n
q
⎟
ρ
ρ
(2.2)The new reactivity ρ1 includes all possible reactivity feedbacks. This result indicates that any change (increase or decrease) in the source intensity, or a reactivity insertion leads to a power change. If for a moment, one neglects the possible reactivity feedbacks (ρ1 = ρ0), the result would indicate that the final power level during a transient is influenced only by the change of the source strength (Schikorr, 2001). On the other hand, if a positive or negative reactivity is inserted, the state of subcriticality will have an influence on the final power level.
Reactivity Feedbacks
An ADSR does not respond to reactivity feedbacks as a critical reactor. The presence of the neutron source has an effect of reducing the sensitivity to reactivity changes, as it was explained through equation 2.2. On the other hand, the strength of the feedback effect depends on the specific fuel design and in particular, the choice of the subcriticality level. When the reactor is more subcritical, more importance is taken by the source and less effect is produced by the reactivity feedbacks. Therefore, to take advantage of the subcritical level, the subcriticality must be carefully balanced with the possible positive reactivity insertions and negative feedbacks. It has been argued that a rearrangement of fuel may lead to critical configurations of the core (Eriksson and Cahalan, 2002). It is therefore of primary concern to increase the Doppler effect in fertile‐free fuel. For this purpose, Eriksson et al., (2005) have studied inherent safety aspects of different fuels and concluded that, the higher melting point of Cermet fuel in combination with its larger critical mass hold the most favourable characteristic for the recriticality issue.
The pumping system has also to be studied against the problem of nuclear stability. If a large bubble passes through the core, a safety margin needs to be provided combining the coupled thermal‐hydraulic and reactivity disturbance. The reactivity effects of the bubble will depend on the void worth throughout the core. If the coolant is lead alloy and for an equal gas mass, the bubble is going to be volumetrically smaller by as much as a factor of ten than in the case of sodium and therefore its reactivity effects are much smaller. For same volumetric bubble size, the consequences may be somewhat less because of the larger flow area used in naturally circulating lead and therefore less resistant to the bubble passage and a shorter transit time. In spite of these facts, to achieve a negative void worth in a liquid metal reactor requires the core design to either be very flat (core diameter much larger than the fuel height) or very tall (fuel height much larger than core diameter). Either configuration results in a high level of neutron leakage and a negative reactivity effect with the assumption of voiding. These approaches move the ADSR design away from the optimum economical configuration and accelerator power requirements. Detailed analysis of postulated events are necessary to support the risk assessment and similarly assess the probability of occurrence. It is desirable to avoid designs that would achieve prompt criticality from a postulated large bubble passing through the core.
Axial thermal expansion of fuel pins and radial thermal expansion of the core subassemblies lead to negative feedbacks. It is still a question whether the negative feedbacks are sufficient to control a reactor excursion, if the proton beam remains on. Other types of safety measures are necessary to assure the control of neutron source transients. The reactor safety strategy for the ADSR needs to be redefined with respect to the conventional fast and thermal reactors.
2.3 Thermalhydraulic Issues
Coolant Type
plans, the choice can be extended by the research and development tasks of various alternatives.
Table 2.2 Liquid metal coolant characteristics
Coolant Advantages Shortcomings
Sodium Suitable neutronics Activity with O2 and H2O
Suitable thermalhydraulics Gamma activity
Not corrosive Medium melting point
Low radiotoxicity
Lead‐Bismuth Suitable neutronics Volatile alpha activity of Po
Suitable thermalhydraulics Highly corrosive
No activity with O2 and H2O Medium melting point
No gamma activity Long radiotoxicity
Lead Suitable neutronics Low alpha activity of Po
Suitable thermalhydraulics High corrosive
No activity with O2 and H2O High melting point
No gamma activity Long radiotoxicity
Lead‐bismuth has been selected as the coolant for the ADSR primarily because of two criteria: performance and safety. LBE offers low moderation, low absorption cross‐section, excellent heat transfer coefficients, high boiling point and low system pressure. The moderation and absorption cross section are important parameters determining the neutronic efficiency of the transmutation process. The low operating pressure reduces the structural requirements to the reactor vessel and the high boiling point minimizes the possibility of positive void reactivity insertions. The freezing point is an important issue for the coolant‐structural interaction and potential failure by flow blockages. For this reason, lead‐bismuth with a lower melting point (400 K) has been preferred as its counterpart “pure lead”, which is cheaper but has higher melting point (600 K).
discarded for the ADSR because of its explosive reaction in contact with air or water. Regarding natural circulation capabilities, Ceballos et al., (2004) have presented a study on liquid metal performance, demonstrating that the flow rate in natural convection systems is a function of the non‐dimensional Stanton number and the Reynolds number. Some of these conclusions will be later exposed in chapter 4, when we analyze the steady‐state reactor operation using dimensional analysis to clarify the nature of buoyancy flows.
Coolant Flow
To avoid loss of flow from a breakdown of the pumps, buoyancy driven cooling systems have been proposed (Rubbia et al., 1995; Ansaldo, 2001). In these systems, the pumping power is determined by the pool configuration such as pool components and vessel height. From a safety perspective, the heat removal with natural circulation could be enhanced with gas lift pumps. This design has good safety characteristics and offers a bigger safety margin during transients (Cheng et al., 2004).
The flow is subjected to a balancing system of buoyant forces and pressure drops. The pressure drops are proportional to the geometrical design of the flow channels and the flow velocity distribution. The core pressure drop is the largest portion of the total system pressure drop and therefore, the core height and diameter is always optimized for fuel economy and required pumping power. In the core, the flow has local characteristics since the power varies with respect to position. This leads to a local maximum fuel pin temperature profile that restrains the maximum core power. Another flow phenomenon is gas entrainment, since it can lead to reactivity insertions. The sources of entrainment could be fission gas release from a fuel pin rupture, a steam generator pipe break‐up with carry‐under or the gas entrainment from the gas covering the pool. The steam generator tube rupture event was identified as a potential source for extensive voiding and according to Eriksson et al., (2005), the nitride and Cermet fuels hold a lower temperature peak during a positive void reactivity excursion. The gas cover entrainment has been studied and predicted for the liquid metal sodium reactor, surface waves and vortex formation by high velocities could result in encapsulation of bubbles carried deep below the coolant surface (Tang et al., 1978).
great part the efficiency of the power cycle. The heat exchanger must permit a safe, stable and reliable operation under all conditions. For the case of a buoyancy cooled reactor, the design should minimize the pressure drop and provide good heat transfer performance. The decisions during design stage regarding secondary coolant type, flow configuration (in tube – in shell) and thermodynamic parameters (inlet ‐ outlet temperature, pressure) are of relevance in the optimization of the natural circulation cooled reactor. The effect of partial flow blockages is important if the flow is obstructed and the cooling capability is lost resulting in a temperature rise and possible coolant boiling as well as cladding failure. Flow cavitation, which is caused by the reduced local pressure below the saturation vapor pressure, can induce vibration and erosion. Hydrodynamics studies of flow transitions have to demonstrate that this problem will not occur at any condition.
Core Power Limits
The maximum operating power level of the ADSR is limited by technical and economical requirements. The intensity of the neutron source necessary to drive the subcritical core depends on the spallation capacity to multiply the neutrons and the degree of subcriticality. The neutron multiplication increases with the increase of keff and also, with the increase of the proton beam energy, because the number of spallation neutrons is increased. Yamamoto and Shiroya (2003) have studied the performance of the neutron multiplication of 3 different target materials, depleted uranium (DU), lead (Pb) and Tungsten (W). The results have demonstrated a considerable impact on the neutron yield. DU provides the higher thermal flux, followed by an slightly higher thermal flux from Pb over W, but, Pb has a smaller absortion cross section than W, giving it a greater multiplication rate.
core, which is limited by the vessel size. Besides, there are other types of technical limitations, which are intrinsic to all type of nuclear reactors such as the maximum fuel and cladding allowable temperatures to withstand thermal stress and strain. The removal of decay heat is another important factor to consider when limiting the maximum power for reactor operation. Decay heat should be transferred to an auxiliary cooling system when emergency conditions occur and the heat exchanger is not available. Some designs propose the decay heat removal by RVACS ‐ Reactor Vessel Auxiliary Cooling System (Davis et al, 2002; Ansaldo, 2001). These operate transferring the heat from the fuel pins to the coolant and then, to the reactor vessel wall, which is cooled by natural convection of air. The radial power profile in the ADSR seems to have a large impact on the power restrictions, due to a higher power density observed around the central region. This effect is increased with the increased of subcriticality level (Rubbia et al., 1995).
2.4 Mechanical Issues
The high neutron flux and the high temperature conditions place severe requirements on materials in the reactor core, particularly to the beam window and the fuel pin cladding. Both provide a containment barrier to radioactivity release. The fuel pins especially provide the basic structural integrity for the fuel elements. The probability of pin failure depends on the internal fuel pin gas pressure and the service conditions during lifetime. The cumulative damage evaluates the damage fraction during the steady and transient conditions for creep and fatigue.
The number of cycles to fatigue failure depends on the stress level and temperature history, the damage effect is usually measured as a reduction on the number of cycles. Fatigue considerations for other structural components exposed to the coolant flow are also important in the safety assessment. The flow distribution and mixing is important to reduce effects of thermal transients to structures. The material strength is dependent on the strain rate at high temperatures and if long time deformations persist, creep fluence occurs. Small strains with large hold times are more damaging than larger strain applied during short periods (Sauzay et al., 2004).
Buongiorno (2001) have limited the maximum vessel height to 19 meters because of transportability reasons, considering that it is an economical advantage if the reactor vessel can be built in a factory and being transported to the plant site. Davis et al., (2002) consider that a higher vessel could reduce the cost adjustment over capital cost if there is an increase on electricity production. Metal degradation due to liquid metal exposure is another important factor in the reduction of mechanical properties of materials. Aiello et al., (2004) have studied the effect of flowing Pb‐Bi alloy on cladding steel T91. The tensile results shows a reduction of ductility and a fractured surface. Penetration of the liquid metal may be one of the reasons for the reduction of mechanical properties. In Russia, steel corrosion protection from Pb‐Bi flows has been done mainly by maintaining a certain concentration of oxygen in the liquid metal, necessary to create a protective film of Fe3O4 on the steel surface (Ilincev, 2002). The irradiation effects are interpreted as irradiation hardening at lower temperatures and recovery at higher temperatures (Uwaba and Ukai, 2004). Irradiation hardening due to neutron displacement creates dislocations, which considerably affect the metal strength.
2.5 Design Preferences
Any reactor has to achieve the best thermal performance keeping some design parameters below certain limits. These limits have been gathered throughout fundamental analysis and experience. A list of design parameters and their limiting values for the ADSR have been introduced in table 2.3. The subdivision in groups relates the parameter to the physical system where it belongs. Due to our impossibility to perform experimental investigations and lack of design experience with liquid metal technology, we have appealed to the literature review, engineering sense and assumptions in order to draw some values.
cladding, structures and fuel are 650 C, 450 C and the fuel melting temperature respectively. Limiting temperatures based on accelerated corrosion effects have been excluded since there was not literature available for this case. Finally, the choice of a suitable subcriticality level is limited to 0.95 < keff < 0.98. This range considers sufficient safety margins to prompt critical excursions as well as accelerator power availability.
Table 2.3 Design limits for the ADSR
Constraints Design limits Reference
Structural Creep strain 1% local ASME
2% in the central line of the cross section ASME
5% in the average cross section ASME
Fatigue σ < τyield ASME
Coolant velocity < 1 ‐ 1.5 m/s corrosion ‐ erosion Fomichenko
< 9 m/s cavitation and vibration Tang
Thermal‐ Cladding Temperature limit normal operation < 650 C Davis
hydraulic Fuel Fuel temperature < melting temp. Davis
overpower conditions 115% Tang
Reactor Vessel temp. steady < 450 C MacDonald
Neutronics Kinetics subcriticality level ‐ 0.95 < keff < 0.98 Rubbia
Reactivity coef. Doppler coefficient < 0
2.6 Safety Constraints
to its boiling temperature; the last in order to avoid positive reactivity insertions. Finally, the reactivity is required to be always negative in order to remain subcritical, any positive excursion that brings the reactor critical or prompt critical is considered as a major loss of control and delivers high risk of accidents.
Table 2.4 Safety limits for the ADSR
Constraints Safety limits Reference
Structural Creep strain 1% local ASME
2% in the central line of the cross section ASME
5% in the average cross section ASME
Cumulative Damage < 1.0 ASME
Fatigue σ < τyield ASME
Cumulative Damage < 1.0 ASME
Creep‐Fatigue Cumulative Damage < D ASME
coolant velocity < 1 ‐ 1.5 m/s corrosion ‐ erosion Fomichenko
< 9 m/s cavitation and vibration Tang
Thermal‐ Cladding Temperature limit transients < 750 C Davis
Hydraulics Temp. limit anticipated transient <788 C Tang
Temp. limit unlikely events transient < 871 C Tang
Fuel Fuel temperature < melting temp. Davis
overpower conditions 110% Tang
Reactor Vessel temp. transients < 750 C MacDonald
Coolant Coolant Temp. < Boiling temperature MacDonald
Neutronics Kinetics Reactivity < 0
2.7 Safety Analysis
consequence of a failure in the secondary cooling circuit are expected events. Emergency events are unlikely faults requiring the shutdown and repair activities, it may involved the reduction of lifetime of components, but, not the break down of structures. In this class, the flow blockages or positive reactivity insertions could be fitted. Faulted events are major incidents of very low probability but involving the risk of complete structural integrity loss, requiring repair activities or extensive inspection. They are large reactivity insertions or the unprotected transients where the control fails in shutting down the proton beam. Analysis of these transients will be later conducted along chapters 4 and 5.
Table 2.5 Classification of scenarios for the safety analysis of the ADSR
TYPE Initiating event Definition
Probability (event/year)
Normal Full power Normal operation 1
Startup Startup
Shutdown Shutdown
Proton beam fluctuations Beam interruptions Several
Upset Decrease of heat removal from heat exchanger partial LOHS 10‐2
Secondary cooling system pump failure LOHS Loss of electrical power in secondary cooling LOHS Proton beam fluctuations Beam interruptions Loss of electrical power in accelerator building Beam trip Loss of electrical power in reactor building LOHS Partial loss of enhanced gas lift with beam partial LOG shutdown Total loss of enhanced gas lift with beam LOG shutdown
Emergency Fuel assembly partial blockage Partial Blockage 10‐2 ‐ 10‐4
small pipe break in heat exchanger and steam Positive reactivity
carry under
Small pin failure with gas release Positive reactivity
Proton beam fluctuations Beam interruptions
Faulted Large pipe break in heat exchanger Positive reactivity 10‐4 x 10‐7
Maschek et al., (2003) have studied ADSR accident scenarios and proposed a system of 3 shutdown levels, which follows the lines of defense concept. The first shutdown level corresponds to the neutron source shutdown, which it will rely only on monitoring and detection systems. A second shutdown level requires the insertion of additional absorber rods. This shutdown level resembles a redundant shutdown system. A third shutdown level relies on inherent and passive measures from the design like selecting the core geometry with favorable reactivity coefficients and assuring reasonable kinetic parameters. The kinetics characteristics of ADSR presented in section 2.2 have demonstrated that it is necessary to manage the neutron source in order to achieve inherent shutdown. Ericksson and Cahalan (2002) have studied the inherent shutdown based only on reactivity feedbacks and proved that it is unfruitful. They have determined that the fastest transients are the overpower transients caused by a maximum insertion of the beam power. Transients without beam shutdown have a severe impact on integrity and some shutdown device is required, therefore, they have proposed some concepts to achieve the passive ADSR shutdown.
A safety strategy that relies on redundant shutdown systems is not sufficient to assure that they will handle all possible transient scenarios. Thus, the implementation of passive safety mechanisms should be at the heart of an integral safety strategy for the ADSR. The development of a reactor safety strategy for the ADSR is especially needed since it is a new innovative and not well‐known combination of different technologies.
2.8 Concluding Remarks
we not laugh? If you poison us, do we not die? and if you wrong us, shall we not revenge?” The Merchant of Venice, W. Shakespeare, 1564‐1616
3 Physical Modeling of the ADSR
3.1 Introduction
During the fission process, energy is deposited in the fuel as heat. The heat conducts through the fuel pin and is transferred to the coolant flowing outside the fuel pin via convection. Figure 3.1 shows the fuel pin temperature gradient as function of the pin radius. As the thermal conductivity is different for the different materials and heat is only generated in the fuel, the temperature profile changes from the fuel zone to the gap and cladding. Cladding Coolant Fuel Gap Figure 3.1 Temperature profile as a function of the radius in a fuel pin with an internal heat generation given from the nuclear fission process
Fuel pin Streaming peripheral tube Streaming centre tube Figure 3.2 Core top view with fuel assemblies distribution (at the left) and fuel assembly design (at the right)
The fuel pins are surrounded by the coolant, which flows in a closed circuit inside the reactor pool. The heat released from the fuel pins in the core heats up the liquid metal, the fluid density decreases and the fluid moves upward. The total buoyancy force is given by density differences between the riser and the downcomer. Figure 3.3 shows a scheme of the reactor pool. It displays the different regions like core, heat exchanger, riser and downcomer. It also includes the power cycle and the gas lift pump system. The gas injected inside the riser, is meant to decrease the fluid density and produce additional buoyancy. The heat exchanger removes the heat from the reactor pool and releases its energy into a conventional power cycle.
Compressor Heat exchanger Riser Turbine Storage tank Condenser Core Downcomer Pump Figure 3.3 Reactor pool with power cycle and coolant flow scheme including the gas lift pump system
The thermalhydraulics model describes the coolant flow in different regions like the core, riser, heat exchangers and downcomer. Its mathematical formulation is based on the momentum and energy conservation laws for a closed loop. The model considers the momentum source provided by buoyancy forces from thermal gradients and two‐phase flow when gas is injected in the riser. The thermalhydraulics model contains three submodels: the heat exchanger, the core and the riser model. It solves the coolant temperature and mass flow rate in the reactor pool given the heat transferred from the fuel pins to the coolant and heat removed by the heat exchanger. The set up of these models is explained graphically in figure 3.4.
FUEL PIN MODEL THERMALHYDRAULIC MODEL
Fuel NEUTRON KINETICS
3.2 Neutronic Model
Introduction
The computation of neutron kinetics is usually obtained by solving the neutron transport equation. The direct solution of the spatial, energy, time dependent equation can be achieved with advanced numerical schemes that provide sufficient accuracy although the computational work is “expensive”. A simpler solution is usually obtained with the exact point kinetics approximation which writes the solution as a product of a spatial function and a time dependent function. The solution method calculates the spatial shape less frequently than the time dynamic response (Ott and Neuhold, 1985).
An alternative solution proposed by Rineiski and Maschek (2005) for the subcritical reactor keeps a single time‐independent weighting function, but employs a variable flux shape. The model offers a table of power shapes computed in the keff mode for the initial conditions and several shapes computed at different reactivity levels. This approach, can improve significantly the speed of the calculations, although perfect agreement with exact point kinetics is never achieved.
The derivation of a simpler point kinetics model assumes that the flux shape never changes in time. Many safety codes apply this simpler and faster point kinetics model for studying transients of critical reactors. The computation of parameters such as reactivity and reactivity coefficients are integrals over the space and can be determined a priori. Eriksson et al., (2005) have investigated the ability of simple point kinetics to predict the transient behavior of an ADSR. Numerical experiments were carried out to compare the precision of point kinetics against the full solution of space‐time dependent kinetics. The results suggested that point kinetics is capable of accurate solutions for transients involving external source perturbations with small flux deformations, because of the uniformity of the reactivity feedbacks. When the transient involves localized perturbations, the results indicates better precision if keff is lower (more subcritical). This behavior is due to the lower sensitivity to the feedback effects and the major role played by the source on the power output.
